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arXiv:cond-mat/0106204 · Physical Review Letters

Particle-Hole Symmetry and the Effect of Disorder on the Mott-Hubbard Insulator

P. J. H. Denteneer, R. T. Scalettar, Nandini Trivedi

Published Sep 18, 2001• 52 citations
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Abstract

The understanding of the interplay of electron correlations and randomness in solids is enhanced by demonstrating that particle-hole ( p-h) symmetry plays a crucial role in determining the effects of disorder on the transport and thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that the low-temperature conductivity decreases with increasing disorder when p-h symmetry is preserved, and shows the opposite behavior, i.e., conductivity increases with increasing disorder, when p-h symmetry is broken. The Mott insulating gap is insensitive to weak disorder when there is p-h symmetry, whereas in its absence the gap diminishes with increasing disorder.

DOI
10.1103/physrevlett.87.146401

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The understanding of the interplay of electron correlations and randomness in solids is enhanced by demonstrating that particle-hole ( p-h) symmetry plays a crucial role in determining the effects of disorder on the transport and thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that the low-temperature conductivity decreases with increasing disorder when p-h symmetry is preserved, and shows the opposite behavior, i.e., conductivity increases with increasing disorder, when p-h symmetry is broken. The Mott insulating gap is insensitive to weak disorder when there is p-h symmetry, whereas in its absence the gap diminishes with increasing disorder.
We prove that the Kane-Mele-Hubbard model with purely imaginary next-nearest-neighbor hoppings has a particle-hole symmetry at half filling. Such a symmetry has interesting consequences including the absence of charge and spin currents along open edges, and the absence of the sign problem in the determinant quantum Monte Carlo simulations. Consequentially, the interplay between band topology and strong correlations can be studied at high numeric precisions. The process that the topological band insulator evolves into the antiferromagnetic Mott insulator as interaction strength increases is studied by calculating both the bulk and edge electronic properties.
Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behavior. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the two-dimensional Hubbard model. Because the charge gap arises from on-site correlations, we have been refining the nonperturbative approach of Matsumoto and Mancini [Phys. Rev. B 55, 2095 (1997)] which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbor energy scale J. At half-filling, we find that the spectral function possesses a gap of order U and is devoid of any coherent quasiparticle peaks although ordering or charge fractionalization are absent. At low temperatures, local antiferromagnetic correlations emerge. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. The breakdown of Luttinger's theorem in the underdoped regime is traced both to the dynamically generated Mott gap as well to a nonvanishing of the imaginary part of the self-energy at the Fermi level. Spectral weight transfer across the Mott gap also emerges as a ubiquitous feature of a doped Mott insulator and suggests that high- and low-energy scales are inseparable. Additionally in the underdoped regime, we find that a pseudogap exists in the single-particle density of states as well as in the heat capacity. The pseudogap (which is set by the energy scale t2/U){t}^{2}/U)t2/U) is argued to be a ubiquitous feature of a lightly doped Mott state and simply represents the fact that hole transport involves double occupancy. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a one-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\ifmmode\pm\else\textpm\fi{}y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level x<1/3.x<1/3.x<1/3. The sign change is tied to a termination of strong correlation physics in the doped Mott state.
We investigate the effects of Coulomb disorder on the half-filled ionic Hubbard model within the framework of dynamical mean-field theory (DMFT), using the equation-of-motion method as the impurity solver, combined with typical medium theory (TMT). In contrast to conventional disordered Hubbard models, the ionic Hubbard model contains a staggered ionic potential that introduces additional competition between band-insulating and correlation-driven insulating tendencies. We analyze how this ionic potential modifies the electronic phases induced by Coulomb disorder through the arithmetic and geometric averages of the local density of states. In the absence of disorder, the system exhibits metallic (M), Mott-insulating (MI), and band-insulating (BI) phases. When Coulomb disorder is introduced, Anderson-insulating (AI) behavior and localized states (LS) inside the Mott gap are also observed. In particular, the LS regime appears between the metallic and Mott-insulating phases at small ionic potentials, whereas the AI regime develops for sufficiently large values of the Coulomb interaction and ionic potential. Our results show that the interplay between ionic potential, electron correlation, and disorder substantially influences the localization behavior and insulating characteristics of the ionic Hubbard model.
We investigate the strong correlation effect in the spinless electron-hole two-band Hubbard model using the dynamical mean-field theory. At half filling, both the renormalization factor ZZZ and the number of conduction electrons (valence holes) ncn_cnc​ decrease with increasing the interband Coulomb interaction UUU down to Z∼0.15Z\sim 0.15Z∼0.15 and nc∼0.1n_c\sim 0.1nc​∼0.1 for $U_c \sim \mbox{bandwidth}$ at which the first-order Lifshitz transition occurs from a correlated semimetal with a large effective mass m∗/m=Z−1m^*/m=Z^{-1}m∗/m=Z−1 to a band insulator with a finite gap due to the Hartree shift. A slight hole doping xxx in the band insulator with a large U>UcU>U_cU>Uc​ yields a remarkable correlated semimetal with Z∼0.1Z\sim 0.1Z∼0.1 at x∼0.01x\sim 0.01x∼0.01, where in-gap states emerge above the valence band top and those weights increase with increasing xxx together with the increase in ZZZ similar to the in-gap states observed in doped Mott insulators.
We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.
We study the nature of electronic states induced by the non-magnetic impurities in a hole-doped Mott insulator. We further examine the consequences of doping on the transport and spectral properties. By employing exact diagonalizaton + Monte-Carlo simulation based on the many-body computational techniques, which allows for the thermal and spatial fluctuations besides a fine resolution in the momentum-space spectral function, the current investigation unravels the degree of localization of the electronic states induced by the impurity atoms as a function of temperature. The major consequences of doping impurity, which introduces holes in the systems, include the appearance of impurity states just above the Fermi level and only in the vicinity of momenta where the gap opens along the normal state Fermi surface in the insulating state. The electronic state at the impurity site is split because of the antiferromagnetic background. The pseudogap-like behavior of the density of states is weakened as reflected by the enhanced charge fluctuations even away from the impurity site at an elevated temperature. Our study also reflects on the degree of improvement in conductivity as well as particle-hole asymmetry introduced in the momentum-resolved spectral function, which maximizes towards the high-symmetry points like ([Formula: see text].